Jiranek and Ridgewell suffered thigh and calf injuries respectively during Tuesday's home Barclays Premier League defeat to Newcastle.
The duo are doubtful for Saturday's FA Cup fifth round meeting with Sheffield Wednesday at St Andrew's, but manager Alex McLeish expects the pair to be available to face Arsenal at Wembley on February 27.
He said: "Jiranek and Ridgewell are struggling for Saturday, but we don't believe it will affect the players in terms of being available for the cup final.
"The injuries are not serious. It is a relief because we would definitely struggling a bit for numbers if we were to lose one or two defenders.
"Defenders since the start of the season was always the worry. We didn't have enough cover. With a few days rest, they should be fine."
Source: PA
Source: PA